This paper considers autonomous robotic sensor networks taking measurements of a physical process for predictive purposes. The physical process is modeled as a spatiotemporal random field. The network objective is to take samples at locations that maximize the information content of the data. The combination of information-based optimization and distributed control presents difficult technical challenges as standard measures of information are not distributed in nature. Moreover, the lack of prior knowledge on the statistical structure of the field can make the problem arbitrarily difficult. Assuming the mean of the field is an unknown linear combination of known functions and its covariance structure is determined by a function known up to an unknown parameter, we provide a novel distributed method for performing sequential optimal design by a network comprised static and mobile devices. We characterize the correctness of the proposed algorithm and examine in detail the time, communication, and space complexities required for its implementation. Copyright © 2011 John Wiley & Sons, Ltd.